Limits of effective potential approach:: Nucleus-electron entanglement in a model of the He+-ion

Entanglement may be considered a resource for quantum information processing, as the origin of robust and universal equilibrium behaviour, but also as a limit to the validity of an effective potential approach, in which the influence of certain interacting subsystems is treated as a potential. Here we show that a closed three-particle ( two protons, one electron) model of a He+-ion featuring realistic size, interactions and energy scales of electron and nucleus, respectively, exhibits different types of dynamics depending on the initial state: For some cases the conventional approach, in which the nucleus only appears as the center of a Coulomb potential, is valid, in others this approach fails due to entanglement arising on timescales as small as 10(-5) s. Eventually, the system can even show signatures of thermodynamical behaviour, i.e. the electron may relax to a maximum local entropy state which is, to some extent, independent of the details of the initial state.